Quantum circuit synthesis typically involves complex number-theoretic computations. A set of quantum gates is selected to serve as a basis, and various basis-specific approaches are used to synthesize a target unitary in the selected basis. Some methods for bases such as the Clifford+T basis, the V-basis, and the Fibonacci anyon basis are available, but these methods are limited to a single basis. In addition, for some bases, it is unclear how to synthesize a target unitary, or if such a synthesis is possible. Synthesized circuits are often based on approximate unitaries that correspond to the target unitary within a specified precision, so that the target unitary is synthesized based on exactly synthesizable unitaries. Unfortunately, conventional synthesis methods are limited in the available selection of bases, and synthesis methods applicable to arbitrary bases are needed.